198 ON A NEW ELLIPTIC ANALYSER. may be reversed (i.e. turned through 180°), and the means of the readings in these four subsidiary positions may be taken for greater accuracy. The readings of the fixed and moveable verniers in each of the two principal positions are four quantities given by observation, which determine four unknown quantities, namely, (1) the index error of the fixed verniers, or, which comes to the same, the azimuth of the major axis of the ellipse described by the particles of ether, measured from a plane fixed in the graduated circle ; (2) the ratio of the axes of the ellipse ; (3) the index error of the moveable verniers ; (4) the retardation due to the retarding plate. The unknown are determined by the known quantities by certain simple formulae given by the author. Let these unknown quantities be denoted by /, tan sr, i, and p, respectively, the latter being reckoned as an angle, at the rate of 300° to an undulation. Let li, r be the readings of the fixed and moveable verniers respectively in one of the principal positions, jK', r the corresponding readings in the other ; then 0 sin (r' — r) tan (?•' — r) cos 2-GT = - -V- -7 -.,,, ' ; cos p = - — 7T>7~~-~y>'\ • sin (R —R) ' tau (If - R) The author stated that he had made a good many observations with this instrument for the sake of testing its performance, and that he had found it very satisfactory. Inasmuch as light is not homogeneous, the illumination never vanishes, but only passes through a minimum, and in passing through the minimum the tint changes rapidly. This change of tint is at first somewhat perplexing ; but after a little practice, the observer is able to point mainly by intensity, taking notice of the tint as an additional check against errors of observation. The accuracy of the observations is a little increased by the use of certain rather pale coloured glasses. To give an idea of the degree of accuracy of which the instrument is susceptible, suppose the ratio of the axes of the ellipse described to be about 3 to 1. In this case the author found that the mean error of single observations amounted to about a quarter or the fifth part of a degree in the determination of the azimuth, three or four thousandths in the determination of the ratio of the